# Tagged Questions

The process of fiting some statistical model to a particular set of data. Mostly done on a computer, and using varied numerical methods such as optimization or numerical integration, or simulation.

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### Tune parameters from a specific equation in R

This is the first time I am truing to tune model parameters in R. I have a fairly complicated equation with multiple parameters: ...
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### Average duplicates before fitting?

Common practice for calibration curves is to take several duplicate measurements for each timepoint (or concentration, whatever variable) and fit using the average of each measurement set. The ...
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### Discrete probability distribution with two 'tails'

I am interested in knowing whether there is any discrete probability distribution similar to Poisson but also extended in the negative value part (i.e., it can take negative values and there is no a ...
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### Setting up maximum likelihood estimation with multi-response data

I was trying to fit the parameters of a time-dependent system coupled of ODES related to a kinetic experiment with multi response data. Example: A->B+H A+H->C+H A->D dcA(t)/dt=-k1Ca(t)-k2Ca(t)*Ch(t)-...
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### Vuong (1989) non-nested test to compare Heckman and Double-hurdle model

I am looking a lightly reading instruction for how to perform Vuong (1989) test to choose the better fit model for a Heckman and a Cragg's double-hurdle model. I've tried this note from Wooldridge ...
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### “Standardizing” a Rayleigh random variable with an offset

I have data that is believed to be Rayleigh distributed (according to some academic papers). However, when I plot the histogram (probability normalized below) it looks like a Rayleigh distribution ...
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### METROPOLIS-HASTINGS with likelihood

I am trying to set up a Metropolis-Hastings algorithm in Matlab in order to estimate the parameters ${\theta}$ (it is a vector of 5 elements) to fit a curve to a set of data $D={X_i,Y_i,\delta_i}$. $X$...
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### neural network for data set with large number of samples

What are the rules of thumb for neural network configurations with large number of samples? I have a dataset with 200k samples, 400 features, and binary label classification problem. How should I ...
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### Fitting data to binomial or bernoulli distributions

I'm trying to fit a count variable to discrete distribution, poisson and negative binomial are not the best candidate to my data since i have only 3 possible values: 0,1 or 2 (sometimes 2) . Can ...
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### Bayesian Confirmatory Factor Analysis: goodness of fit indexes

I'm trying to fit a Bayesian Confirmatory Factor Analysis with R. R seems to have excellent packages like 'blavaan' and 'MCMCpackage' which enable users to fit bayesian CFA and I have fit some models. ...
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### How can I compare model fit of LASSO versus OLS?

I want to compare the accuracy of a linear model which uses three predictors and which I estimate with OLS with a model which uses alternative predictors and which I estimate with LASSO. Number of ...
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### Neural network input values belonging to classes

I need help on configuring a neural network. I would like to pass in accelerometer values (x,y,z) from two different sensors, and have the network compute the corresponding angle. I am providing close ...
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### Why is the arithmetic mean smaller than the distribution mean in a log-normal distribution?

So, I have a random process generating log-normally distributed random variables $X$. Here is the corresponding probability density function: I wanted to estimate the distribution of a few moments ...
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### Estimating correlation(covariance) matrix when fitting a copula using R copula package [migrated]

I have a question about the R package copula. When using fitCopula to fit a copula to data, ...
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### Fit a Gaussian to data with R with optim and nls

I want to fit a Gaussian to the following data: ...
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### Fit tail to monotonically decreasing data

I am trying to fit several distributions to monotonically decreasing data, and pick the one that fit the best based on several criteria, e.g. mle estimate. I am able to do this by fitting a curve to ...
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### Combining the results of 4 fits performed on 4 different dataset

I have 4 dataset which are independent measurement of the same physical quantity. I have fitted each dataset with a certain model, as a result of the fit I estimated one parameter with its uncertaity (...
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### Obtaining Probability for costs above a certain threshold: probability, cdf, distribution fitting

I never sought for help on a forum since I feel that many times the answer for a problem can be found if one reads books and searches for long enough in publications. But I would be very grateful if ...
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### Bayesian MCMC Fitting

I am doing a Bayesian MCMC fit using emcee in python. I first maximize the log of the likelihood and use the results as initial parameter starting points in my MCMC. I am using a uniform prior and ...
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### Nuisance Parameter in Bayesian MCMC

I am doing a Bayesian MCMC fit to some data using a simple model and I want to understand how to handle nuisance parameters. I am looking at this tutorial. The model is a line: $$y = m x + b$$. The ...
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### How to take dataset uncertainty into account in distribution fitting?

If we have a dataset like x=(3,4,2,1,4,...,5), we have classic methods (method of moments, maximum likelihood method, etc) to fit a distribution. However, in certain real life cases, we can have ...
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### Fitting of the parameters of non-linear regression

I can fit the data with non-linear function, namely Mechanistic Growth curve from the JMP library. See the example of the fit in the next figure. The fit equation is BA = a(1 - b e-c *PA). BA ...
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### Formulate equation after fitting to log(y)~x) using lm() [duplicate]

Following code was used to fit a function to my data; ...
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### How to improve the fit of a zero-inflated, negative binomial glmmADMB model

I have been trying to fit count data that is zero-inflated and overdispersed using generalized linear mixed models. My research led me to the glmmadmb function in the glmmADMB package. I am fitting ...
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### How to fit a discrete distribution that can only be sampled from to count data?

My question is similar to this one. Assume we have a distribution from which we can only sample, but have no information on its pmf and consider further some count data: ...
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### Quadratic fitting raw time series data vs linear fitting its derivative

I have time series data $f_i(t_i)$. Is there a difference between the following two strategies: Fitting $\hat{f}(t)=at^2+bt+c$ to the original data Fitting $\hat{g}(t)=2at+b$ to the time derivative ...
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### How to find best fitting with this data in r? [duplicate]

I have this data, data frame fit1: fit1 x y 1 0 2.36 2 1 1.10 3 2 0.81 4 3 0.69 5 4 0.64 6 5 0.61 I would find the best exponential fit of the data, how i ...
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### Why model data using parametric distributions instead of empirical?

I've been wondering why the use of empirical distributions in research is not as prevalent as I think it should be given my understanding (likely misinformed) that an empirical distribution would give ...
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### Validating log-log fit

I'm trying to build a predictive model with my data. I selected the log-log transformation with the idea that it could tame the heteroskedasticity in the data set and it appeared to do so well. ...
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### Measuring how well a new vote fits to a model of existing votes

My knowledge in statistics is very limited, so I hope this is actually an easy question. I am working on a kind of survey application where users either vote between a finite number of discrete ...
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### Bootstrapping a fitted distribution

The following code fits a normal distribution to vector V1 of length 56, and then boostraps and plots the bootstrapped values of parameters. I would like to be certain my understanding of this is ...
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### Estimating Distributions of Weighted Data

I'm trying to build a bivariate copula-based model of income and wealth in Italy and I'm having trouble handling weighted data. I have access to micro data, a survey of about 10,000 households that ...
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### Reg-Arima fitted estimates more flexible than forecast

I am fitting a regression model with ARMA errors, and comparing its fitted and forecasted values with a linear regression. I am wondering why a reg-ARMA appears to have a much better fitted estimate ...
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### Fit a straight line in 3D with 3D uncertainties

So I'm trying to extend the recipe given here in chapter 7 to 3 dimensions. I have x,y,z data points each with their own uncertainties and I'm trying to fit a straight line. So I'm extending the the ...
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### Which model(s) are appropriate for this kind of data

So, I tried to implement a model on some data. The dependent variable is a ratio that can get higher than 1, is lower bounded by zero and, seeing figure 1, is left skewed.Thus, a logit regression is ...
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### Compare inferred parameters

Given one set of data I fit the same model in two different ways. I now have the inferred values for the parameters and the standard error. How can I test if they are statistical different? I have ...
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### Linear Regression Analysis with heavy tailed noise

I have 5 data sets, each can be fitted (this is given) with a linear model $y=a+x b+\epsilon$ but of different parameters $a,b$, where $\epsilon$ is a heavy-tailed noise of mean zero and $x$ dependent,...
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### How to select the thresold in Generalized Pareto distribution

I'm using generalized Pareto distribution to fit the tail data, I want to know is there any computational way to estimate the threshold parameter as we do in estimating the sigma et shape using MLE? ...
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### fitting t distribution with lighter tails

I am trying to fit a t distribution in R using the fitdistr function in the MASS package as follows ...
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### How to determine which factor rotation gives the best model fit? [duplicate]

I have to use factor analysis to determine if it fits my data adequately. I am wondering how rotations play into it. What am I looking for when I change the rotation? The p-value is the same so how I ...
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### Confidence bound of fitted function

I'm dealing with fitting function to data set and with interpretation of such fit and I'm working with Matlab 2011b. Suppose we have fitted function in form $y=f(a_i,x_j)$ where $a_i$ are parameters ...
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### Error in Linear Regression Parameters: Using mean measurement vs. all measurements

I have a set of measurements y taken at 17 different values of x, with 50 repeated measurements at each value of x. They follow a simple linear relationship y = mx + c, and I am fitting the parameters ...
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### Single fitted parameter from multiple data

Let's say I have to perform more than one non-linear fit over experimental replicates, each of them being an exponential decay (y <- 50*exp(-Ax)). What I'm doing ...
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### optim() convergence in fitting gamma distribution to separate peaks of time series data

Trying to fit gamma distribution to each separate peak of time series data (chromatography). As a peak i take local minimum-maximum-minimum part of the data each time. Since the peaks values do not ...
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### Fit raw data to distribution and use chi-square

I have a dataset of number of tweets over time similar to this: ...
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### How do you fit a Poisson distribution to table data?

I've been given a table of $x=(0,1,2,3,4,5,6)$ and $y=(3062,587,284,103,33,4,2)$, which are such that the number of $x_i$ tells an amount of children that all $y_i$s have. I'm asked to fit a Poisson ...
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### Visualizing 3-D fit

I have two independent variables, call them X and Y, and I have to fit a dependent variable Z = f(X,Y) somehow. In an experiment, the experimentalist measured Z as a function of X, and another ...
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### model fit in logistic regression

I have developed a model for simple logistic regression with 1 independent ordinal variable and 4 binary independent variables. The model gives 64% correctly predicted cases, a Nagelkerke r2 of 12% ...